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For Exercises 41–54, write the equation in the form
. Then if the equation represents a
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College Algebra
- Show how to find the equation otthe containing the points (2,1,-2), (-3,-8, 4) & 12,3,1).arrow_forwardDo the points (1, 5, −7), (1, 7, −10), and (1, 8, −13) lie on the sameline?arrow_forwardRecall that an equation of a circle can be written in standard form (x-h)² + (y-k)² = r, where (h, k) is the center and r is the radius. After expanding both squares, moving all terms to the left-hand side, and combining like terms, the equation can also be written in the form x² + y² + Ax+By+ C = 0, where A, B, and C are constants. a. Find an equation of the form x2 + y² + Ax+By+C =0 for the circle that passes through the points (6, 0), (2, 2), and (7,-3). To do so, find the values of A, B, and C by writing and solving a system of 3 linear equations. System: Show the steps of solving the system. Equation in Standard Form: Solution: b. Rewrite the equation found in part (a) in standard form using the technique of completing the square. c. Use your result in part (b) to determine the center and radius of the circle. Center: A = B = C = Radius:arrow_forward
- find the equation of the line through p (1,3,2) and Q(2,1,1). All answers are integersarrow_forwardThe figure shows that the points (6, 12) and (8, 10) lies on a circle represented by the equation(x−h)2+(y−k)2=r. Given that h = 0, how would you use (6, 12) and (8, 10) to find the values of k and r? Write two equations that you can use to find the values of k and r.arrow_forwardSketch v = (−2, 1), w = (2, 2), v + 2w, v − 2w.arrow_forward
- Find the value of m if the points (5, 1), (-2, -3) and (8, 2m) are collineararrow_forward#3 It must be in the format of the second picture.arrow_forwardA billiards table is 8 feet by 4 feet, and has pockets in all four corners and in the middle of the two longer sides; we can visualize this as a rectangle in R2 and assume that the bottom left pocket is at the origin and the top right pocket is at (8, 4). A ball starts at the point (1, 2) and is hit in the direction ⟨5, −2⟩. Does the ball go into a pocket before it bounces off three walls and, if so, which one?arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL